Please help!!!!!The speed of the current in a river is 6 mph. A ferry operator who works that part of the river is looking to buy a new boat for his business. Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. He has a boat in mind, but he can only test it on a lake where there is no current. How fast must the boat go on the lake in order for it to
serve the ferry operator's needs?
Answers
The boat must go 9mph on the lake in order for it to serve the ferry operator's needs
Represent the speed of the boat on the lake or in still water with x
Given that:
The current in a river has a speed of 6 mph.
- When the boat goes upstream, the speed is x - 6;
- When the boat comes downstream, the speed is x + 6;
So, the time taken by the boat each trip are:
The equation that calculates the required time (x) is:
This gives
Expand
Evaluate the like terms
Divide through by 9
Collect like terms
Factorize
Solve for x
x cannot be negative.
So, we have:
Hence, the boat must go 9mph on the lake in order for it to serve the ferry operator's needs
Read more about speed and distance at:
Answer: the speed of the boat on the lake is 9 mph
Step-by-step explanation:
Let x represent the speed of the boat on the lake or in still water.
The speed of the current in a river is 6 mph. This means that if the boat goes upstream against the speed of the current, its total speed would be (x - 6)mph. If the boat goes downstream against the speed of the current, its total speed would be (x + 6)mph.
Time = distance/ speed
Every day, his route takes him 22.5 miles each way against the current and back to his dock, and he needs to make this trip in a total of 9 hours. This means that the time taken to travel upstream is
22.5/(x - 6). The time taken to travel downstream is
22.5/(x + 6)
Since the total time is 9 hours, it means that
22.5/(x - 6) = 22.5/(x + 6)
Cross multiplying, it becomes
22.5(x + 6) + 22.5(x - 6) = 9
Multiplying through by (x + 6)(x - 6), it becomes
22.5(x - 6) + 22.5(x + 6) = 9[(x + 6)(x - 6)]
22.5x - 135 + 22.5x + 135 = 9(x² - 6x + 6x - 36)
22.5x + 22.5x = 9x² - 324
9x² - 45x - 324 = 0
Dividing through by 9, it becomes
x² - 5x - 36 = 0
x² + 4x - 9x - 36 = 0
x(x + 4) - 9(x + 4) = 0
x - 9 = 0 or x + 4 = 0
x = 9 or x = - 4
Since the speed cannot be negative, then x = 9
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Hi, I need help pretty plz! If anyone has the right answers, plz share! Thank u! (Screenshots below)
What is the height of this cone?
Multiplying a trinomial by a trinomial follows the same steps as multiplying a binomial by a trinomial. Determine the degree and maximum possible number of terms for the product of these trinomials: (x2 + x + 2)(x2 – 2x + 3).HOW DO I Explain how it arrived at your answer?
How much of the apples did Lucy use for her dessert?
Answers
Get the whole fraction.
3 2/3 = ((3*3) + 2) / 3 = 11/3
1 1/3 = ((3*1) + 1) / 3 = 4/3
Original weight of apples = 11/3
Remaining weight of apples = 4/3
weight of apples used = ?
Subtracting fractions:
Step 1. Make sure the denominator are the same
11/3 - 4/3
Step 2. Subtract the numerators and put the difference above the denominator
(11 - 4) / 3 = 7/3
Step 3. Simplify the fraction
7/3 = 2 1/3
for 20 words also 0+0
Answers
Answer:
no problem :)
Step-by-step explanation:
Answers
Answer:
the answer is: {x|x>0}
Answers
y=2x+6
sub 2x+6 for y
3x-(2x+6)=6
3x-2x-6=6
x-6=6
add 6
x=12
sub
y=2x+6
y=2(12)+6
y=24+6
y=30
x=12
y=30
(x,y)
(12,30)
soltion is (12,30)
event. If x represents the cost for each snack gift basket and
y represents the cost for each chocolate gift basket, what is the cost
for each chocolate gift basket?
(1) $20 (3) $30
(2) $25 (4) $54
Answers
Answer:
$30
Step-by-step explanation:
Solving the equation given simultaneously to get the x and y variable;
6x + 5y = 300... (1) × 1
3x + 7y = 285... (2) × 2
Using elimination method, we will multiply equation 1 by 1 and equation 2 by 2 as shown above to have;
6x + 5y = 300... 3
6x + 14y = 570... 4
Subtracting equation 3 from 4, we have;
5y-14y = 300-570
-9y = -270
y = 270/9
y = 30
Since y represent the cost for each chocolate gift basket, the cost of each chocolate gift basket will be $30
Multiply the second equation by -2, then subtract it from the first equation. It should be
6x+5y=300
-6x-14y=-570
-9y=-270
y=30
8x-y=-13
6x-3y=15
Answers
Substitute this in so:
6x-3(8x+13)=15
6x-24x-39=15
-18x-39=15
-18x=54
x=-3
Substitute x into 1st equation:
Y=(8*-3)+13
Y=-24+13
Y=-11